Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
| direct product | D11×#392 |
| Fitting | C11×#392 ⋊ C2 |
| Sylow | C11 ⋊ C2×#392 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D11 |
| commutator, socle, cosocle | C23×C11 | C24 |
| Fitting | C11×#392 | C2 |
| hypercenter | #392 | D11 |
| hypocenter | C11 | C2×#392 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ #392 | |
1812 conjugacy classes of subgroups; only the 223 normal subgroups are shown.
This group has 1812 conjugacy classes of subgroups — too many to draw. Only its 223 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
154 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#1343, #14664427, D11×#1595, … |
| maximal normal subgroup of | D11×#1343, #14664427, D11×#1595, … |
| maximal quotient of | D11×#1438, D11×#1439, D11×#1444, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7704);